Binary input distributions are often assumed when studying the reliable rates of communications systems, either through channel capacity or other related metrics. The widespread analysis of binary inputs follows from their tractability and optimality, or near optimality, at low Signal to Noise Ratio (SNR) under varying amounts of receiver channel state information (CSI). Rates are considered to be reliable if the probability of decoding error can be made arbitrarily small by increasing the code length in communications over a discrete-time Rayleigh flat-fading channel. It is assumed that the transmitter can select among the class of binary input distributions, and that imperfect (or partial) CSI is available at the receiver.
When perfect receiver CSI is available, it is well known that antipodal signaling (BPSK) maximizes the capacity of this channel among binary inputs. Conversely, without CSI at the receiver, On-Off keying (OOK) has been shown to be capacity maximizing. However, when only imperfect receiver CSI is available, it is not clear as to which strategy, even among these two, is optimal.